Global attitude/position regulation for underwater vehicles

A nonlinear controller is designed for a 6 DOF model of an unmanned underwater vehicle (UUV) which includes both the kinematics and the dynamics. It is shown how the use of a Lyapunov function consisting of a quadratic term in the velocity (both linear and angular), a quadratic term in the position and a logarithmic term in the attitude leads to a design of a control law that achieves global asymptotic stabilization to an arbitrary set point in position/attitude. The control law is made linearly bounded by avoiding cancellation of some of the quadratic nonlinearities in the model. No information about the inertia matrix, the damping, and the Coriolis/centripetal parameters is used in the controller, endowing it with a certain amount of parametric robustness. The control law is given in terms of the modified Rodrigues parameters. An extensive simulation study shows that the proposed control law achieves excellent tracking for slowly changing trajectories, even though it is designed only for set point regulation. The nonlinear controller dramatically outperforms a linear controller.